Let the coordinate A(x1,y1),B(x2,y2) and C(x3,y3) According to question, x-coordinate as well as y coordinates are in GP. Let x1=a,x2=ar and x3=ar2, y1=b1y2=br and y3=br2 Now, A(a,b),B(ar,br),C(ar2,br2). Slope of AB=‌
b(1−r)
a(1−r)
=‌
b
a
and Slope of BC=‌
br(1−r)
ar(1−r)
=‌
b
a
As slope of AD− Slope of BC ∴A,B and C are collinear. ∴A,B and C lie on a straight line.